WBJEE · Maths · Definite Integration
The value of the integral \(\int_{1}^{5}[|x-3|+|1-x|] d x\) is equal to
- A 4
- B 8
- C 12
- D 16
Answer & Solution
Correct Answer
(C) 12
Step-by-step Solution
Detailed explanation
\(\int_{1}^{5}[|x-3|+|1-x|] d x\) \(=\int_{1}^{5}|x-3| d x+\int_{1}^{5}|1-x| d x\) \(=\int_{1}^{3}|x-3| d x+\int_{3}^{5}|x-3| d x+\int_{1}^{5}|1-x| d x\) \(=\int_{1}^{3}-(x-3) d x+\int_{3}^{5}(x-3) d x\) \(+\int_{1}^{5}-(1-x) d x\)…
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